3.13.34 \(\int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx\)

Optimal. Leaf size=78 \[ -\frac {1000 (3 x+2)^{13}}{28431}+\frac {925 (3 x+2)^{12}}{2187}-\frac {14390 (3 x+2)^{11}}{8019}+\frac {66193 (3 x+2)^{10}}{21870}-\frac {10073 (3 x+2)^9}{6561}+\frac {1813 (3 x+2)^8}{5832}-\frac {49 (3 x+2)^7}{2187} \]

________________________________________________________________________________________

Rubi [A]  time = 0.03, antiderivative size = 78, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \begin {gather*} -\frac {1000 (3 x+2)^{13}}{28431}+\frac {925 (3 x+2)^{12}}{2187}-\frac {14390 (3 x+2)^{11}}{8019}+\frac {66193 (3 x+2)^{10}}{21870}-\frac {10073 (3 x+2)^9}{6561}+\frac {1813 (3 x+2)^8}{5832}-\frac {49 (3 x+2)^7}{2187} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^7)/2187 + (1813*(2 + 3*x)^8)/5832 - (10073*(2 + 3*x)^9)/6561 + (66193*(2 + 3*x)^10)/21870 - (14
390*(2 + 3*x)^11)/8019 + (925*(2 + 3*x)^12)/2187 - (1000*(2 + 3*x)^13)/28431

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin {align*} \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx &=\int \left (-\frac {343}{729} (2+3 x)^6+\frac {1813}{243} (2+3 x)^7-\frac {10073}{243} (2+3 x)^8+\frac {66193}{729} (2+3 x)^9-\frac {14390}{243} (2+3 x)^{10}+\frac {3700}{243} (2+3 x)^{11}-\frac {1000}{729} (2+3 x)^{12}\right ) \, dx\\ &=-\frac {49 (2+3 x)^7}{2187}+\frac {1813 (2+3 x)^8}{5832}-\frac {10073 (2+3 x)^9}{6561}+\frac {66193 (2+3 x)^{10}}{21870}-\frac {14390 (2+3 x)^{11}}{8019}+\frac {925 (2+3 x)^{12}}{2187}-\frac {1000 (2+3 x)^{13}}{28431}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 74, normalized size = 0.95 \begin {gather*} -\frac {729000 x^{13}}{13}-261225 x^{12}-\frac {5100570 x^{11}}{11}-\frac {3110589 x^{10}}{10}+122655 x^9+\frac {2623581 x^8}{8}+155453 x^7-51908 x^6-\frac {390396 x^5}{5}-20140 x^4+8688 x^3+6912 x^2+1728 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

1728*x + 6912*x^2 + 8688*x^3 - 20140*x^4 - (390396*x^5)/5 - 51908*x^6 + 155453*x^7 + (2623581*x^8)/8 + 122655*
x^9 - (3110589*x^10)/10 - (5100570*x^11)/11 - 261225*x^12 - (729000*x^13)/13

________________________________________________________________________________________

IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3, x]

________________________________________________________________________________________

fricas [A]  time = 1.16, size = 64, normalized size = 0.82 \begin {gather*} -\frac {729000}{13} x^{13} - 261225 x^{12} - \frac {5100570}{11} x^{11} - \frac {3110589}{10} x^{10} + 122655 x^{9} + \frac {2623581}{8} x^{8} + 155453 x^{7} - 51908 x^{6} - \frac {390396}{5} x^{5} - 20140 x^{4} + 8688 x^{3} + 6912 x^{2} + 1728 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x, algorithm="fricas")

[Out]

-729000/13*x^13 - 261225*x^12 - 5100570/11*x^11 - 3110589/10*x^10 + 122655*x^9 + 2623581/8*x^8 + 155453*x^7 -
51908*x^6 - 390396/5*x^5 - 20140*x^4 + 8688*x^3 + 6912*x^2 + 1728*x

________________________________________________________________________________________

giac [A]  time = 0.97, size = 64, normalized size = 0.82 \begin {gather*} -\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x, algorithm="giac")

[Out]

-729000/13*x^13 - 261225*x^12 - 5100570/11*x^11 - 3110589/10*x^10 + 122655*x^9 + 2623581/8*x^8 + 155453*x^7 -
51908*x^6 - 390396/5*x^5 - 20140*x^4 + 8688*x^3 + 6912*x^2 + 1728*x

________________________________________________________________________________________

maple [A]  time = 0.00, size = 65, normalized size = 0.83 \begin {gather*} -\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(3*x+2)^6*(5*x+3)^3,x)

[Out]

-729000/13*x^13-261225*x^12-5100570/11*x^11-3110589/10*x^10+122655*x^9+2623581/8*x^8+155453*x^7-51908*x^6-3903
96/5*x^5-20140*x^4+8688*x^3+6912*x^2+1728*x

________________________________________________________________________________________

maxima [A]  time = 0.61, size = 64, normalized size = 0.82 \begin {gather*} -\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x, algorithm="maxima")

[Out]

-729000/13*x^13 - 261225*x^12 - 5100570/11*x^11 - 3110589/10*x^10 + 122655*x^9 + 2623581/8*x^8 + 155453*x^7 -
51908*x^6 - 390396/5*x^5 - 20140*x^4 + 8688*x^3 + 6912*x^2 + 1728*x

________________________________________________________________________________________

mupad [B]  time = 0.08, size = 64, normalized size = 0.82 \begin {gather*} -\frac {729000\,x^{13}}{13}-261225\,x^{12}-\frac {5100570\,x^{11}}{11}-\frac {3110589\,x^{10}}{10}+122655\,x^9+\frac {2623581\,x^8}{8}+155453\,x^7-51908\,x^6-\frac {390396\,x^5}{5}-20140\,x^4+8688\,x^3+6912\,x^2+1728\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3*(3*x + 2)^6*(5*x + 3)^3,x)

[Out]

1728*x + 6912*x^2 + 8688*x^3 - 20140*x^4 - (390396*x^5)/5 - 51908*x^6 + 155453*x^7 + (2623581*x^8)/8 + 122655*
x^9 - (3110589*x^10)/10 - (5100570*x^11)/11 - 261225*x^12 - (729000*x^13)/13

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 71, normalized size = 0.91 \begin {gather*} - \frac {729000 x^{13}}{13} - 261225 x^{12} - \frac {5100570 x^{11}}{11} - \frac {3110589 x^{10}}{10} + 122655 x^{9} + \frac {2623581 x^{8}}{8} + 155453 x^{7} - 51908 x^{6} - \frac {390396 x^{5}}{5} - 20140 x^{4} + 8688 x^{3} + 6912 x^{2} + 1728 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**6*(3+5*x)**3,x)

[Out]

-729000*x**13/13 - 261225*x**12 - 5100570*x**11/11 - 3110589*x**10/10 + 122655*x**9 + 2623581*x**8/8 + 155453*
x**7 - 51908*x**6 - 390396*x**5/5 - 20140*x**4 + 8688*x**3 + 6912*x**2 + 1728*x

________________________________________________________________________________________